Question

a) 0,(7);
r) 0,5(12);
6) 0,(19);
A) 0,(13);
B) 0,2(3);
e) 0,2(6).

Answer 1

$1) \ 0,(7)= \dfrac{7}{9}\\\\\\2) \ \ 0,5(12)=\dfrac{512-5}{990} =\dfrac{507}{990} =\dfrac{169}{330} \\\\\\3) \ \ 0,(19)=\dfrac{19}{99} \\\\\\4) \ \ 0,(13)=\dfrac{13}{99} \\\\\\5) \ \ 0,2(3)=\dfrac{23-2}{90}=\dfrac{21}{90} =\dfrac{7}{30}\\\\\\6) \ \ 0,2(6)=\dfrac{26-2}{90} =\dfrac{24}{90} =\dfrac{4}{15}$